Geometry of Banach Spaces and Related Fields

Cover Title page Contents Preface A Few Lines on Per Enflo’s Works References On the Quasi-greedy Basic Sequence Problem 1. Introduction and preliminaries 2. Partial unconditionality and partial symmetry 3. Extraction principles for quasi-greedy bases 4. Extraction principles for almost greedy bases 5. Existence of truncation quasi-greedy basic sequences References On Properties of Geometric Preduals of Classical Smoothness Spaces 1. Introduction 2. Basic Definitions 3. Geometric Preduals 4. Finiteness Principle 5. Simultaneous Extension 6. Approximation Property 7. Biduality Property References On Norm-attaining Mappings on Banach Spaces 1. Introduction 2. Norm Attaining Mappings 3. Bishop-Phelps-Bollobás property 4. Pointwise Bishop-Phelps-Bollobás property 5. Applications to the Daugavet property 6. The numerical radius attainment and its applications to the numerical index Acknowledgment References Translation Invariant Banach Function Spaces and Fourier Multiplier Operators 1. Introduction 2. Preliminaries 3. Translation invariant Banach function spaces 4. The homogeneous part of a translation invariant B.f.s. 5. Multiplier operators 6. Convolution operators via measures 7. Vector measures associated with convolution References Cycle Spaces: Invariant Projections and Applications to Transportation Cost 1. Introduction 2. Invariant and minimal projections onto cycle spaces for different families of graphs Acknowledgment References The Finest Locally Convex Module Topology 1. Introduction and preliminaries 2. Main results Acknowledgements References Derivations with Values into Bimodules of τ-measurable Operators 1. Introduction 2. Preliminaries 3. Derivations with values in an ideal of a von Neumann algebra 4. Derivations with values into symmetric spaces (of possibly unbounded operators) References Singular Integrals in Uniformly Convex Spaces 1. Introduction 2. Set-up 3. Dyadic cubes 4. A dyadic decomposition of finite kernels 5. Estimates for Haar coefficients 6. Extracting paraproducts 7. Reorganisation of the remaining parts 8. Final estimates 9. Concluding remarks Acknowledgments References Some Easily Formulated Open Problems in Banach Space Theory 1. Introduction 2. Asplund spaces; C1-Fréchet differentiability 3. C^{k}-Fréchet differentiability 4. Gâteaux differentiability 5. Rotund renormings 6. General structure 7. Schauder bases 8. Operators 9. Nonlinear analysis Acknowledgments References Geometry of Trinomials Revisited 1. Introduction 2. Geometry of polynomial spaces of low dimension 3. One specific example: The space P_{n}(R) with n=2 and n=3 4. The space P_{m,n}(R) References Metric Invariants in Banach and Jordan–Banach Algebras 1. Introduction 2. A taste of radicals in Banach and Jordan-Banach algebras 3. Sets of invertible elements as a metric invariant 4. The geometric goodness of C*- and JB*-algebras 5. A geometric tool: preservers of inverted Jordan triple products 6. Unitary elements as a metric invariant Acknowledgments References Back Cover